Final answer:
To find the height of the stainless steel patio heater, which is a square pyramid, use the Pythagorean theorem on the right triangle formed by the slant height, half the base, and the height of the pyramid.
Step-by-step explanation:
The student is asking about the height of a stainless steel patio heater, which is in the shape of a square pyramid. Given the length of one side of the base, 23.8 inches, and the slant height, 90.1 inches, they would like to determine the vertical height of this pyramid. Finding the height of a pyramid involves using the Pythagorean theorem in the context of the pyramid's geometry, specifically within the right triangle formed by the height, half the base, and the slant height.
First, calculate the length of half the base, which is half of 23.8 inches. Then, use the slant height and this value to form a right triangle. The Pythagorean theorem states that the square of the hypotenuse (the slant height in this case) is equal to the sum of the squares of the other two sides (half the base and the height). From this, you can solve for the height by isolating the height term and taking the square root. The final height can then be found mathematically, providing the answer to the student's question.